An improved example for an autoconvolution inequality
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915436373737472 |
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| author | Boyer, Christopher Li, Zane Kun |
| author_facet | Boyer, Christopher Li, Zane Kun |
| contents | We give a nonnegative step function with 575 equally spaced intervals such that $$\frac{\|f \ast f\|_{L^{2}(\mathbb{R})}^{2}}{\|f \ast f\|_{L^{\infty}(\mathbb{R})}\|f \ast f\|_{L^{1}(\mathbb{R})}} \geq 0.901564.$$ This improves upon a recent result of Deepmind's AlphaEvolve, which found a nonnegative step function with 50 equally space intervals for which the left hand side is $\geq 0.8962$. Our function was found using simulated annealing and gradient based methods rather than using large language models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_16750 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An improved example for an autoconvolution inequality Boyer, Christopher Li, Zane Kun Classical Analysis and ODEs Combinatorics Number Theory We give a nonnegative step function with 575 equally spaced intervals such that $$\frac{\|f \ast f\|_{L^{2}(\mathbb{R})}^{2}}{\|f \ast f\|_{L^{\infty}(\mathbb{R})}\|f \ast f\|_{L^{1}(\mathbb{R})}} \geq 0.901564.$$ This improves upon a recent result of Deepmind's AlphaEvolve, which found a nonnegative step function with 50 equally space intervals for which the left hand side is $\geq 0.8962$. Our function was found using simulated annealing and gradient based methods rather than using large language models. |
| title | An improved example for an autoconvolution inequality |
| topic | Classical Analysis and ODEs Combinatorics Number Theory |
| url | https://arxiv.org/abs/2506.16750 |